There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{({r}^{2} + {x}^{2})}^{3}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3}{2}r^{4}x^{2} + \frac{3}{2}r^{2}x^{4} + \frac{1}{2}r^{6} + \frac{1}{2}x^{6}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3}{2}r^{4}x^{2} + \frac{3}{2}r^{2}x^{4} + \frac{1}{2}r^{6} + \frac{1}{2}x^{6}\right)}{dx}\\=&\frac{3}{2}r^{4}*2x + \frac{3}{2}r^{2}*4x^{3} + 0 + \frac{1}{2}*6x^{5}\\=&3r^{4}x + 6r^{2}x^{3} + 3x^{5}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！